Under the overarching banner of Conservatism, we have:
Liberal conservatism
Conservative liberalism
[u]Libertarian conservatism[/u]
Fiscal conservatism
National and traditional conservatism
Cultural and social conservatism
Religious conservatism
Progressive conservatism
Authoritarian conservatism
Now I understand that the "Religious Conservatives" are a little backward, but if you check out under the Libertarian Conservatism there is a group called the [url=https://en.wikipedia.org/wiki/Christian_libertarianism]Cristian Libertarians[/url] that would probably make more sense to you.
Political beliefs shouldn't be seen as monoliths. Everything falls along a spectrum, and it may not be as far away from what you think and feel as you may have imagined.